Authorities in the north-east United States are warning of a new crisis facing the region as cold weather heads towards tens of thousands of people who still have no power or heat and are living in homes damaged by superstorm Sandy.

While much of New York City is approaching a semblance of normality, state governor Andrew Cuomo and the city's mayor Michael Bloomberg said on Sunday that plummeting temperatures were now one of the main threats facing residents in other stricken areas such as Staten Island and Long Island.

Cuomo warned of a "massive, massive housing problem", with up to 40,000 people – mainly residents of public housing – needing relocating because of damage from the storm and the lack of electricity and heat.

"People are in homes that are uninhabitable," Cuomo told reporters at a press briefing. "It's going to become increasingly clear that they're uninhabitable when the temperature drops and the heat doesn't come on."

Fuel shortages are also having an impact on people with back-up generators. "There are continuing issues with the fuel delivery and fuel distribution system," he said.

But he added that "there has been improvement, [and] there will be more improvement."

The White House has sanctioned the release of an additional 12m gallons of unleaded fuel and 10m gallons of diesel. Much of that gas was being trucked to New Jersey and New York throughout the weekend.

In the worst-hit areas of New York and New Jersey, which are still suffering six days after Sandy hit, there is growing anger among residents at the official response.

In the Rockaways, an oceanfront section of Queens, Bloomberg was barracked by people as he toured the devastation over the weekend. Thousands there are still without power, and have been told they may remain so for days to come.

"When are we going to get some help?" one woman shouted during an angry confrontation on Saturday.

City officials have turned to opening warming shelters in preparation for a drop of temperatures overnight.

Elderly people were being urged to move to these temporary homes. Meanwhile, about 25,000 blankets were being handed out to those who refused to move.

But many believe the measures represent too little, too late, with some residents accusing the city of forgetting them in the rush to get the lights back on in the financial centre of lower Manhattan.

"Nothing right is going on here. There's old ladies in my building that have got nothing," one resident told Bloomberg during his walkabout in the Rockaways. In a one-to-one with the mayor, the man complained: "This is the first drop-off site over the bridge, [and] we can't even get a bottle of water or a hot chocolate."

Bloomberg promised that help was at hand, insisting that he understood their grievances.

"I spoke with many people who were worried and frustrated and cold," the mayor said at a press briefing Saturday. "There is no power there and temperatures are dropping. Even those who have generators are having a hard time getting fuel."

Gas shortages could continue for days, New Yorkers were told Sunday. Throughout the weekend, lines of cars queued up at pumps across New York. In neighbouring New Jersey, governor Chris Christie imposed rationing to cope with the scarcity of gas.

At least 10 arrests have so far been made in relation to confrontations and line jumping at petrol stations.

While parts of Staten Island and remote parts of Queens continue to struggle with blackouts, Manhattan is on its way to being restored to business as usual.

Schools are due to reopen on Monday after a week out, and much of the subway will be running, though Cuomo warned commuters that the system may struggle to cope with the weight of traffic. "There's been major progress but it's not going to be normal tomorrow," he said.

"South Ferry station, which had been a large fish tank, has now been pumped dry," he added.

Cuomo also warned utilities firms that they would be held accountable for any delays that could have been prevented.

"I want them to provide the service that they get paid to perform," he said, adding: "We will be reasonable, but we will hold them accountable."

Bloomberg echoed governor Cuomo's call on utilities firms to up their game.

"We urge them to commit more resources to get power back to the Rockaways," the mayor said in an update on recovery efforts.

Bloomberg also stressed the need to keep warm and check on vulnerable neighbours who made need help.

"It is cold outside and it will remain cold in the coming days. It is critical that people stay warm," he said in a Sunday afternoon press briefing.

He spoke of an "enormous outpouring" of donations of clothes and food from members of the public but added that money sent to the Mayor's Fund would do more good at this stage as charity organisations were at capacity.

Power had now been restored to all but 145,000 people across New York City. But 19,000 homes in the Rockaways – one of the worst hit areas – remained without electricity.